## Area Under a Curve

What is the area of the shaded region in the graph shown? Note the figure is not to scale.

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__**Hint**

**Hint**

Solve the definite integral of the slope while setting the lower and upper bound limits to determine the specified area under the curve.

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__**Hint 2**

**Hint 2**

The power rule:

$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$

Solving the definite integral of the slope while setting the upper and lower bound limits will determine the specified area under the curve.

$$$A=\int_{3}^{6}2x^{2}dx$$$

Recall the power rule:

$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$

Thus,

$$$A=\frac{2}{3}x^{3}\bigg\rvert_{x=3}^{x=6}= \frac{2}{3}(6^{3}-3^{3})$$$

$$$=\frac{2}{3}(189)=126$$$

126